In this talk we consider Stochastic dynamical systems with jumps. Large deviation results for finite dimensional stochastic differential equations with a Poisson noise term have been studied by several authors, however for infinite dimensional models with jumps, very little is available. The goal of this work is to develop a systematic approach for the study of large deviation properties of such infinite dimensional systems. Our starting point is a variational representation for exponential functionals of general Poisson random measures and cylindrical Brownian motions. The representation is then used to give a general sufficient condition for a large deviation principle to hold for systems that have both Brownian and Poisson noise terms. Finally we give examples to illustrate the approach.